You taught me the courage of stars before you left...
tl;dr: When the discrete log $a$ of $a\cdot G$ is known to lie in a small range $[m)$, the baby-step giant-step (BSGS) algorithm recovers $a$ in $\ceil{\sqrt{m}}$ $\Gr$ additions using only a precomputed table of exactly $\ceil{\sqrt{m}}$ compressed points, trading the $O(1)$ time of the naive $m$-sized lookup table for much less memory. This post describes vanilla BSGS, and two…
tl;dr: Running some secp256k1 MSM benchmarks.
tl;dr: The good: Audit went well. Lúcás Meier’s Cait-Sith threshold ECDSA protocol seems like a reasonable, conservative choice. The bad: Near’s MPC currently works in a 5 out of 8 setting, without any proactive refresh. Notes Good MPC’s configuration is transparent, on-chain $\Rightarrow$ can monitor for suspicious membership changes “uses the Cait-Sith protocol in a secure manner”1 “we did not…
tl;dr: Groth’s non-interactive distributed key generation paper[^Grot21e], which uses a novel approximate ZK range proofs to argue correct chunking, but inadvertantly increases share decryption time.
tl;dr: a few notes on Move (and maybe on Aptos too).
tl;dr: This is a “note to self” that there’s some interesting work out there on malleable NIZKs[^CH20]$^,$[^DaEFplus23e].
tl;dr: Some notes to self on state-of-the-art witness encryption (WE) schemes. $ \def\adp{\mathsf{ADP}} \def\aadp{\mathsf{AADP}} \def\eval{\mathsf{eval}} \def\x{\mathbf{x}} \def\M{\mathsf{M}} \def\A{\mathbf{A}} \def\B{\mathbf{B}} \def\R{\mathbf{R}} \def\Rvss{\mathcal{R}_\mathsf{vss}} \def\Radp#1{\mathcal{R}_\mathsf{adp}^{#1}} \def\span{\mathsf{span}} \def\Fbar{\bar{\F}} $ $ \def\stmt{\mathbf{x}}…
tl;dr: What has happened in quantum computing over the years.
tl;dr: A catalog of polynomial commitment schemes for multilinear polynomials (i.e., multivariate polynomials where each variable has degree at most 1). These are the workhorse of modern SNARKs based on the sumcheck protocol.
tl;dr: Collecting some resources.